The degree of nilpotency of
a ring R is defined to be the supremum of the orders of nilpotency of its
nilpotent elements and it is denoted by ν(R). We consider the degree of
nilpotency of the ring of m × m matrices Rm over a ring R. We obtain given
results concerning the degrees ν(Rm) for distinct m’s, in the case R has no
nonzero two-sided annihilators. It is shown that if )⊃ (Rm) = m for some m,
and if R′ is a ring containing R as an ideal such that R′ has no nonzero
two-sided annihilators of R, then ν(Rm′) = m. An application of this result is
given.
